Some revisited results about composition operators on Hardy spaces

We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ a...

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Detalles Bibliográficos
Autores: Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé, Rodríguez Piazza, Luis
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/46376
Acceso en línea:http://hdl.handle.net/11441/46376
https://doi.org/10.4171/RMI/666
Access Level:acceso abierto
Palabra clave:Blaschke product
Carleson function
Carleson measure
Composition operator
Hardy-Orlicz space
Nevanlinna counting function
Schatten classes
Descripción
Sumario:We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on HΨ; construction of a surjective symbol whose composition operator is compact on HΨ and, moreover, is in all the Schatten classes Sp(H2), p > 0. On the other hand, we revisit the classical case of composition operators on H2, giving first a new, and simplier, characterization of closed range composition operators, and then showing directly the equivalence of the two characterizations of membership in the Schatten classes of Luecking and Luecking and Zhu.